On MR. P's humidifier, it states that
When the outside temperature is -20 degrees, you should set the humidifier at 15%;
When the outside temperature is 0 degrees, you should set the humidifier at 25%;
When the outside temperature is 20 degrees, you should set the humidifier at 35%;
(1) What should Mr. P set the humidifier at when the outside temperature is 7 degrees?
(2) Determine the equation that relates the Humidifier setting H
to the outside temperature T.
(3) The highest setting on Mr. P's Humidifier is 45%.
At what outside temperature should he use this setting?
Solution to the Problem:
The answers are:
(1) 28.5%
(2) H = T / 2 + 25
(3) T = 40 degrees.
First solve for the general equation relating H to T.
Consider the three sets of ordered pairs (T, H): (-20, 15), (0, 25), (20, 35).
These three coordinates fall on a line since the slope is the same between any two points.
The slope is 1/2.
The second ordered pair gives the y-intercept (when T = 0, H = 25).
Therefore the equation is H = 1/2 T + 25.
Now use the equation to solve for parts (1) and (3).
(1) H = 7/2 + 25 = 28.5%.
(3) 45 = T / 2 + 25, so T = 40.
Correctly solved by:
| 1. John C. Funk | Ventura, California |
| 2. Judi Breault | Tucson, Arizona |
| 3. David & Judy Dixon | Bennettsville, South Carolina |
| 4. Dylan Martin |
Mountain View High School, Mountain View, Wyoming |